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# Accession Number:

## AD0648173

# Title:

## ON A SINGULAR POINT OF BRIOT-BOUQUET TYPE OF A SYSTEM OF TWO ORDINARY NONLINEAR DIFFERENTIAL EQUATIONS.

# Descriptive Note:

## Technical summary rept.,

# Corporate Author:

## WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

# Report Date:

## 1966-06-01

# Pagination or Media Count:

##
142.0

# Abstract:

## The singular points of Briot-Bouquet type of a system of ordinary nonlinear differential equations written in the form x dwdx hx, w, h0, 0 0, have been studied by diverse authors since C. H. Briot and J. C. Bouquet. Here, w is an n-dimensional column vector and hx, w is an n-dimensional column vector function holomorphic and bounded in x, w in a neighborhood of 0, 0. However, as far as I know, it has not yet been studied, except for n 1, when the eigenvalues of the matrix h sub w 0, 0 are all zero. In this note the author studies the case for n 2 under certain hypotheses. For convenience, the paper is divided into three parts. Part I is concerned with the construction of a formal transformation. In Part II formal solutions are constructed of diverse types depending on two arbitrary constants. Part III considers the analytical meaning of each of those formal solutions. Author

# Distribution Statement:

## APPROVED FOR PUBLIC RELEASE

#